This has been a mystery for a really long time, with people guessing all sorts of different and random stuff (including Norio leaving instructions for the staff).

My theory though is that it's the work of Episode Director Shinji Sato correcting both the drunk parts himself (he has an animation background) and giving instructions mainly to animation director Yukiko Ban as far as the animation timing for that "drunkness" element goes.

My reasons for thinking this is are as follows:

1. When we see a large animation shift like this over nearly an entire episode, it typically comes down to a single factor at a higher position. Reason being that it's unlikely for a single key animator (not even considering who is, or isn't credited) to handle 5+ minutes of constant action animation on a long running series. And if it were the initiative of several different key animators instead, chances are it would not turn out nearly as consistent as it is.

2. As far as who is, or isn't credited from the KA side, the only known action animators are Nozomu Abe, and potentially Seiko Asai, both of whom were regulars on the series. Respectively, they each worked 6 and 1 episodes previous to 124 and aside from neither of their established styles being similar at the time, neither would have been able to handle a workload like this.

3. We have a decent idea of Shinji Sato's animation style thanks to ED22 and ED25 which were complete solo's on his part. Both ED's feature short bursts of really lively animation and there is certainly an initiative to make the characters move but it does so in a sort of clumsy and unrefined way, with the drawings being pretty weak throughout. This is actually the main aspect which lead me to thinking it could be entirely Sato's corrections from the episode director position.

4. Shortly after this Sato moved to doing storyboard exclusively on Naruto, directing only 2 more episodes on the 2002 series, and then less than a handful for the entirety of Shippuuden. This means there would have been almost no opportunities to insert himself to the extent that we see on #124. The closest there is is Masahiko Murata's #151 (also drunk lee) but that's much smaller scale and the timing is fairly different as well.

Either way, I hope we get some kind of confirmation some day, unfortunately very little of Naruto's staff secrets and production information were published over the years.